What do we mean when we say “Math is a language?”
When we see some mathematical notation we’re not familiar with, or if someone is telling us about a math thing and using terminology we haven’t learned, there’s an unfortunate tendency to think, I don’t understand this because I’m not intelligent enough. But imagine if we applied the same standards to language. When you hear someone say something in a language you don’t speak, you don’t think I don’t understand that because I’m not smart enough, you think, I don’t understand that because I don’t speak that language.
And the same applies to math. When we see notation we’ve never seen before, that’s equivalent to a foreign alphabet that we can’t read. When someone is explaining math to us and using terminology we’re not familiar with, or maybe those are words we’ve heard before but we don’t fully understand their usage because we’re not quite fluent in that language, we shouldn’t immediately come down hard on ourselves for simply not knowing something.
Now, you might say, but this isn’t just a foreign language I’ve never studied before, I had years and years of math studies in school, and I still don’t understand it. After so many years of learning, I should understand this. But just as it is with foreign languages, you could study a language in school a couple times a week for years, and after a while you might understand lone words and know a few choice songs but still not speak fluently. This is because becoming fluent in an additional language requires an immersive experience, surrounding ourselves with people who speak that language, practicing every single day, which is not what we get in a standard math education in school. And even if we do that for several years, we might still not quite feel as comfortable in that language that isn’t our mother tongue. That’s the nature of language learning and the human mind. The metaphor holds for math.